Abstract

When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position-dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell’s law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.

Figures (5)

Schematic representation of general refraction. When a surface between two media introduces a phase shift Φ(x) depending linearly on x, the refraction angle is different than that given by the standard Snell’s law.

Diffraction angles for λ=8μm, d=15μm, silicon input medium, and air output medium. The m=0 line and m=+1 lines correspond to normal and general refraction, respectively. Shaded regions correspond to negative refraction.